数学杂志2026，Vol.46Issue(2)：97-119,23.
一类多维随机微分方程的对数截断EM方法
LOGARITHMIC TRUNCATED EM METHOD FOR A CLASS OF MULTI-DIMENSIONAL STOCHASTIC DIFFERENTIAL EQUATIONS
黄永杰 1赵君一郎1
作者信息
- 1. 西南交通大学数学学院,四川成都 611756
- 折叠
摘要
Abstract
This paper studies the problem of preserving positivity in the numerical solution of a class of multi-dimensional stochastic differential equations(SDEs).By modifying the assumptions in the original theory and combining the properties of logarithmic transformation,a new method for constructing truncation functions is developed.The strong convergence result of this numerical method is obtained,and it is proved that the Lp convergence of the numerical solution holds under certain conditions,with the strong convergence rate reaching the 1/2 order.The results of the original method are generalized,successfully expanding the application scope of the logarithmic truncation EM method from scalar SDEs to multi-dimensional SDEs.关键词
多维随机微分方程/保正性/对数截断EM方法/数值模拟Key words
multi-dimensional stochastic differential equations/positivity preserving/the logarithmic truncated EM method/numerical simulation分类
数理科学引用本文复制引用
黄永杰,赵君一郎..一类多维随机微分方程的对数截断EM方法[J].数学杂志,2026,46(2):97-119,23.
